Stator assembly for single phase induction motor



June 2, 1970 J. A. HOUTMAN 3,515,919

STATOR ASSEMBLY FOR SINGLE PHASE INDUCTION MOTOR Filed July 26, 1968 1N VENTOR. Jae/f A .Houzman,

3 4 5 TIME IN SECONDS United States Patent 3,515,919 STATOR ASSEMBLY FOR SINGLE PHASE INDUCTION MOTOR Jack A. Houtman, Holland, Mich., assignor to General Electric Company, a corporation of New York Filed July 26, 1968, Ser. No. 747,870 Int. Cl. F16c 9/06, 23/00 US. Cl. 310166 12 Claims ABSTRACT OF THE DISCLOSURE A stator assembly for a single phase induction motor in 'which by compacting preselected main winding coil sides, which share slots with starting winding coil sides, and distributing turns of the two windings in a predetermined manner, increased locked rotor torque may be attained. The number of turns of wire in the main and starting coils are preselected so that the algebraic product of the third harmonic effective main and starting winding turns is in the range from a relatively small positive number to a relatively large negative number and the algebraic product of the fifth harmonic effective main and starting winding turns is in the range from a relatively small negative number to a relatively large positive number.

BACKGROUND OF THE INVENTION Field of the invention This invention relates generallyto single phase induction motors of the distributed winding type, and more particularly to an improved stator assembly therefor.

Description of the prior art Single phase, alternating current induction motors of the distributed winding type conventionally include a main field winding and a starting field winding, the two windings being angularly displaced on the stator core and being energized, respectively, by phase-displaced currents, in order to provide a torque at zero speed, referred to as locked rotor torque (LRT). The phase displacement of the main and starting winding currents is conventionally provided by the incorporation of dissimilar impedance in the respective winding circuits. In one form of single phase induction motor, referred to as resistance-split, the starting winding is wound to have a higher resistance than the main field winding and may have additional resistance connected in series therewith, the difference in the resistance of the respective main and starting winding circuits thus providing the requisite phase displacement. In another common form of single phase induction motor, the phase displacement is provided by means of a capacitor coupled in series with the starting winding. In some single phase motors, the starting winding is disconnected from the circuit and is thus de-energized when the motor reaches a predetermined speed, as by a speedresponsive switch or a current-responsive relay. In other motors, particularly of the capacitor-start type, the starting winding and its associate capacitor remain in the circuits, such motors being referred to as being of the per manent-split capacitor type.

It is desirable to provide a locked rotor torque as high as possible. An increase in locked rotor torque has commonly been accomplished by increasing the phase displacement between the main and starting winding currents. In the case of motors of the permanent-split capacitor type, this has required the use of a larger, and thus more expensive, capacitor, thus resulting in a significant increase in the total cost of the motor. It is thus desirable to increase the locked rotor torque without an accom- "ice panying significant increase in the overall cost of the motor.

In Pat. No. 3,200,317 to Allen A. Brammerlo, assigned to the assignee of the present application, there is disclosed a stator winding arrangement for use in a single phase induction motor which provides an increase in the starting or locked rotor torque by the distribution of the currents in wires forming the coils of the main and starting windings. In Pat. No. 3,348,183 to Ralph D. Hodges and Francisco C. Avila, and assigned to the assignee of the present application, there is disclosed a method of compacting an insulated coil.

SUMMARY OF THE INVENTION It is accordingly an object of the invention to provide an improved stator assembly for a single phase induction motor.

Another object of the invention is to provide a stator assembly for a single phase induction motor of the distributed winding type which provides increased locked rotor torque over that provided by prior stator assemblies.

In carrying out the objects of the invention in one form, an improved stator assembly for a motor provides a sig nificant increase in locked rotor or starting torque without an accompanying increase in overall cost. A first winding is disposed in predetermined slots in a stator core member and forms a predetermined number of first poles. In addition, a second winding is accommodated by the core member and forms a predetermined number of second poles angularly displaced by a predetermined amount from the first poles. At least one side of certain coils of a first pole is arranged to share a selected slot with a side of a coil of a second pole. The number of turns of wire in the first winding coils and in the second winding coils are preselected so that the algebraic product of the third harmonic effective first and second winding turns is a minimum (e.g., in the range from a relatively small positive number to a relatively large negative number), and the algebraic product of the fifth harmonic effective first and second winding turns is a maximum (e.g., in the range from a relativel small negative number to a relatively large positive number).

By way of exemplification, the number of turns of wire in the coils are preselected to that in the formula:

Where ALRT=change in locked rotor torque n=order of harmonic K =positive constants, functions of n, for a given design N =etfective first winding turns for the n harmonic N =M sin Iraq-I-M sin na M sin na M =number of turns in the respective first coil a /2 the coil pitch angle of the respective first coil in fundamental electrical degrees N =effective second winding turns for the n harmonic S =number of turns of the respective second coil 5 /2 the coil pitch angle of the respective second coil in fundamental electrical degrees, with the factor K N N being a minimum or the factor K N N being a maximum. The slected slot is substantially filled with wire forming the coil sides and at least one side of at least one of the first pole coils in a selected shared slot has a space factor of at least BRIEF DESCRIPTION OF THE DRAWINGS The above mentioned and other features and objects of this invention and the manner of attaining them will 3 become more apparent and the invention itself will be best understood by reference to the following description of an embodiment of the invention taken in conjunction with the accompanying drawings, wherein:

FIG. 1 is a cross-sectional view, partially schematic, illustrating a single phase, alternating current induction motor stator core member and its windings circuitry incorporating the preferred embodiment of the present invention;

FIG. 2 is an enlarged fragmentary view of one of the coil-accommodating slots of the stator core member of FIG. 1, showing compaction of a side of one of the main winding coils prior to installation of a side of a starting winding coil in the slot; and

FIG. 3 is a graph illustrating a representative locked rotor torque curve for the stator member of FIG. 1, and a locked rotor torque curve for a comparable prior art stator member.

DESCRIPTION OF THE PREFERRED EMBODIMENT Referring now to FIG. 1 of the drawing, the present invention is shown as applied to the stator assembly for a two pole permanent-split capacitor start single phase induction motor. The stator assembly, generally indicated at 10, comprises a stator core member 11 conventionally formed of a stacked plurality of relatively thin laminations of magnetic material. The stator core member 11 includes a yoke portion 12 having a plurality of equally spaced-apart teeth 13 extending radially inwardly from yoke portion 12 to the fine winding slots 14 therebetween. The inner ends 15 of teeth 13 mutually define a bore 16 for receiving the usual squirrel-cage rotor (not shown). In the illustrated embodiment, stator core member 11 is provided with twenty-four equally spaced-apart winding slots 14.

In the illustrated embodiment, a main running field winding is provided disposed in certain predetermined slots 14 so as to form two diametrically opposite main poles aligned on the axis shown by the dashed line 17. The main winding is divided into two sections 18a and 18b, each forming one of the main poles, and each comprising five concentric coils of progressively greater pitch. More particularly, the five coils of the main windings 18a and 18b are respectively designated M M M M and M Considering the main winding section 18a, the smallest pitched coil M is positioned in slots 14a and 14b equally spaced on opposite sides of the axis 17 with slots 14c and 14d therebetween. The second main coil M is positioned in slots 14:: and 14 coil M is positioned in slots 14g and 14h, coil M is positioned in slots 14i and 14 and coil M is positioned in slots 14k and 14l. The main winding coils M thru M of the other main winding section 18b are similarly positioned in corresponding slots 14, as shown in FIG. 1. Each of the slots 14 is shown as having a conventional slot insulator 19 therein.

The sides of each main winding coil positioned in the respective pair of slots 14 are joined by end turns projecting from the respective opposite faces of the core member 11, as shown schematically at 20a and 20b in FIG. 1. Further, the main winding coils M through M of each section 1 811 and 18b are interconnected in series in conventional fashion, as shown schematically at 22. In the illustrated embodiment, the two main winding sections 18a and 18b are connected in parallel. Thus, one end of coil M of section 18a is connected to a first external lead 22,, and an end of coil M is connected to the other external lead 23, and likewise an end of coil M of section 18b is connected to external lead 23 and an end of coil M is connected to lead 22 as shown.

An auxiliary or starting field winding is similarly disposed in predetermined slots 14 and forms two auxiliary poles which are respectively angularly displaced from the main poles by a predetermined angular amount. In the illustrated exemplification the two windings are distributed to provide a nonquadrature type winding arrange- =ment. That is to say, the radial centerline for the auxiliary winding poles are displaced on the stator core from the centerlines of the adjacent main winding poles at electrical angles other than ninety electrical degrees. More specifically, the starting winding is divided into two sections 24a and 24b which respectively form the diametrically opposite auxiliary poles which are aligned on the axis shown by the dashed line 25. Each of the starting winding sections 24a and 24b comprises four concentric coils of progressively greater pitch respectively designated as S S S and S More particularly, as will be seen in FIG. 1, one side of the larger pitched starting winding coils S and S are the sole occupants of slots 14c and 14d, the other sides of coils S and 8.; respectively sharing slots 14] and 14b with one side of main winding coils M and M Further, one side of the smaller pitched winding coils S and S respectively share slots 14c and 14a, with the other sides of the main winding coils M and M and the other sides of the start winding coils S and S respectively share slots Hi and 1411 with one side of main winding coils M and M as shown. It will be seen that the other sides of main winding coils M and M are the sole occupants of slots 14g and 14 i, and that the main winding coils M are the sole occupants of slots 14k and 14l.

The sides of the starting winding coils S through 8.; of each of the starting win-ding sections 24a and 24b are joined by end turns extending outwardly from each face of the stator core 11, as shown schematically at 26a and 27a. The concentric coils S through 8.; of each of the starting winding sections 24a and 26b are connected in series in conventional fashion, as shown schematically at 27, and the two sections 24a and 24b are in turn connected in series, as shown schematically at 28. One end of coil S of start winding section 24b is connected to external lead 23 while one end of coil S of starting winding section 24a is connected to external lead 29 to which external starting capacitor 30 is connected. In a permanent-split capacitor motor circuit, capacitor 30 is permanently coupled to external lead 22,, as shown by the dashed line 31, it being readily understood that a speedresponsive switch or a current-responsive relay may be employed for opening connection 31 when the motor has reached a predetermined speed.

The air gap magneto-motive force (MMF) due to the concentric coils of the main and starting windings can be described mathematically as a Fourier series of space harmonics. In the illustrated embodiment in which both poles formed by each winding are alike and are symmetrical about their respective axes 17 and 25, and in which each coil of the respective windings carries the same current, the Fourier series consists of a fundamental frequency term and an infinite series of odd order space harmonics; the windings have both half-wave and quarter wave symmetry and thus only the odd order harmonics exist. For the main winding 18 of the illustrated embodiment, the Fourier series would be:

4 MMF =I cos (MN cos 0+N cos 30+ +N cos n0] where:

I =Root Mean Square (RMS) main winding current amperes w=line radian frequency t=timesec.

0=air gap angle measured from radial centerline of main poles-fundamental electrical degrees n=order of harmonic (2) N fundamental effective main turns=M sin 04 M sin a M sin u (3) N =third harmonic effective main turns=M sin 3ot +M sin 311 --{-M sin 311 5 (4) N n harmonic effective turns=M sin ltoq-l-M sin na +M sin na u /z coil pitch angle of the p coil-fundamental electrical degrees M =No. of turns in the p coil A similar expression can be written for the start winding:

4 MMFstar1= 5 COS (wt-Hy) [Nl g COS B 3es OS nes S where:

I =RMS start winding currentamperes 'y=Angle of time displacement between main and start current 18=Air gap angle measured fro-m centerline of start polesfundamental electrical degrees (6) N =fundarnental effective start turns=S sin 61+S2 sin 62+ '+S Sin s etc.

(7) N =n harmonic effective start turns=S sin ne i-S sin 115 +S sin nd S =Start turns in q coil o /z coil pitch angle of the q coilfundamental electrical degrees It can be shown that the change in locked rotor torque (LRT) is given by:

where K represents a positive constant for a given design.

For the twenty-four slot, two pole stator of the illustrated embodiment having five coil main poles and four coil auxiliary poles, Equations 2 and 6 become:

The expressions for the third and fifth harmonic effective turns from the Equations 4 and 7 are:

Equations 9 and 10 above show that there are many combinations of numbers of turns for the main winding coil M thru M and for the starting winding coils S thru 8.; that will yield the same values of fundamental effective main turns N and fundamental effective start turns N It will be readily seen from Equation 8 above that in order to maximize the value of LRT, it would be advantageous to arrange the turns of the main and starting winding coils so as to make the product N N as negative as possible, and to make the product N5 N5 as positive as possible, etc.

In the past, it has not been possible to obtain the advantages of winding turn distribution indicated by Equation 8 due to space limitations in the stator core member slots, particularly slots which are shared by at least one side of both the main and starting winding coils. For example, a 30-frame, 24-slot, 2-pole stator havinga winding circuit and arrangement shown in FIG. 1, and incorporating the teachings of the aforesaid Brammerlo patent, as the following turn distribution:

M1 M2 M3 M4 M6 S S S3 S4 21 38 48 56 N1eg=142.8

The main winding coils of the stator were formed of copper wire and were non-compacted having a space factor of approximately 75%, space factor being calculated as 100 times the ratio of the circular-mil area of the insulated wires to the circular-mil area defined by the inside of the slot liner and a straight line tangent across the stator bore side of the wires, as shown by the dashed line 32v in FIG. 2.

The winding harmonics of the windings of the above stator, expressed as a percent of the fundamental effective turns, were found to be:

This stator, when tested with a conventional squirrel cage rotor, was found to have a locked rotor torque of 8.8 ounce-feet.

The present invention employs an extension of the teaching of the aforesaid Brammerlo patent in that the number of turns of the main winding coils M thru M preferably progressively increase from the smallest pitched coil M to at least the next-to-largest pitched coil M and the number of turns of the starting winding coils progressively increases from the smallest pitched coil S to the largest pitched coil S Further, in accordance with the invention, preselected sides of the main winding coils which share a slot 14 with the side of a starting winding coil are compacted after being positioned in the slots, but before positioning of the respective start winding coil side in the same slots, in order to increase the space factor to at least Referring particularly to FIG. 2, the side 33 of a main winding coil, after being positioned in a slot 14 of the stator core member 11, as by use of a conventional gun winder or conventional coil injection apparatus, is com pacted as by means of a suitable tool 34 which applies radially outward force upon the coil side 33 toward the closed end of the slot, e.g., toward the bottom of slot 14 and in the direction shown by the arrow 35. As shown in FIG. 2, and as further described in the aforesaid Hodges et al. patent, the application of substantial compacting force upon the coil side formed of a plurality of insulated wires will form the individual wires from their original substantially circular section into non-circular, polygonal cross-section, without injury to the wire insulation, thereby substantially reducing the voids between the individual wires and substantially increasing the space factor. It -will be readily apparent that the compacting force required will be less when insulated aluminum wire is employed than will be required in the case of copper wire. In the case of a 30-frame, 24-slot stator core having the slot configuration shown in FIG. 1, it has been found that 16 gage insulated aluminum wire in part for the main winding coils can be compacted in the slots to provide an 80% space factor with the application of approximately a compacting force of 6500 lbs. per square inch, and to provide a space factor by the application of the compacting force of approximately 11,000 lbs. per square inch.

In accordance with the invention, the same SO-frame, 24-slot, two-pole stator of the exemplification was one with the winding configuration shown in FIG. 1 and with the following distribution of main and starting winding coilturns:

39 Nlu =59.82

Si S2 S3 S4 18 33 46 63 Nle!=142.1

Referring to the corresponding harmonics for the stator having the uncompacted windings, as set forth above, it will be seen that in reducing the product N N from +3849 to +9.29, that product has been rendered more negative, i.e. less positive, and likewise that in increasing the product N N from 3.32 to +252, that product has been rendered more positive. This stator, when tested with the same conventional squirrel cage rotor, provided a locked rotor torque of 10.1 ounce-feet, an increase of approximately over that of the motor having the uncompacted windings. It will be understood that the sign in connection with the product N N and the product N N indicates its relationship to the fundamental product.

In another stator employing the same -frame, 24-slot, twopole stator core member and winding configuration, the following distribution of main and starting winding coils was employed:

S1 S2 S5 S4 20 36 Nice =141.8

With at least one side of the M through M main coils compacted to approximately a 90% space factor before placement of the starting Winding coils S through S the following winding harmonics were found:

Here, it will be seen that the product N N has been rendered still more negative and that the product N N has been rendered still more positive, the resulting locked rotor torque being 11.2 ounce-feet.

FIG. 3 shows the comparison of the locked rotor torque for the stator described above (curve A) providing an average of 10.1 ounce-feet and with the same stator having uncompacted main windings described above indicated providing 8.8 ounce-feet (curve B).

It will be seen that the number of turns of wire in each of the main and starting winding coils is preselected so that the algebraic product of the third harmonic effective main and starting winding turns is in the range from a relatively small positive number to a relatively large negative number, as compared with the corresponding noncompacted main winding, and likewise that the algebraic product of the fifth harmonic effective main and starting winding turns is in the range from a relatively small negative number to a relatively large positive number, again in comparison with the corresponding uncompacted main winding. It will be seen that the slots 14 which are shared by sides of main and starting winding coils are substantially filled with wire, compaction of at least one side of the main winding coils in the shared slots thus permitting the employment of more turns on the smaller pitched coils of the main windings while still accommodating the requisite number of turns of the starting winding coils. This revised main winding distribution made possible by a compaction of the main winding coil sides results in a more positive main winding third harmonic space MMF, which produces a more positive sixpole torque when combined with the negative third harmonic starting winding space MMF, a similar effect likewise being provided in the case of the fifth order harmonic field. I have found that the efiect of this revised main winding distribution and the performance of the motor at other than low speeds is very small, and in particular that there is little effect upon the third harmonic dip.

Thus, in accordance with the invention, and referring again to FIG. 1 of the drawings, it will be seen that for the non-quadrature winding distribution of the illustrated exemplification, the sides of the main winding coil M and M would share slots. The main coils in 14a and 142 usually do not require compaction whereas the main coils in 14b and 14 With sides of start winding coils S and S respectively, are compacted. In addition, the sides of main winding coils M and M which share slots 14k and 14 with the sides of start winding coils S and S respectively, are likewise compacted. Of course, stators having quadrature type winding distributions (i.e., approximately 90 electrical degrees between radial centerlines for adjacent poles of different phases), can also readily incorporate the present invention and obtain the same advantages mentioned above in connection with the illustrated embodiment. Generally speaking in order to derive unusually good benefits from the present invention, the turns should be distributed as already discussed and at least one side of the main winding coils sharing slots with coil sides of the auxiliary winding, especially the intermediate coils of the main winding poles, should be compacted in the slots at least to an slot space factor. If desired, of course, all main winding coil sides could be compacted to provide the at least 80%. This would be quite advantageous when it is desired to provide an unusually high number of turns in the outermost coils of each main winding pole which do not normally share slots with sides of auxiliary winding coils. The outermost coils for a given pole could be divided into two or more coil sections connected in series, with the first section initially being placed into the slots, compacted and then the second section being disposed into the same slots to obtain an unusually high slot space factor, among the other benefits. This latter approach also has the advantage of permitting the use of different materials (e.g., copper and aluminum) for the two coil sections in the same slot. By using aluminum for the first placed coil section and incorporating a greater number of turns in that section than in the second one which may be formed of copper, lower compacting pressures may be employed in the particular slots While realizing economies in the manufacture of the stator without adversely affecting the rated performance of the unit. Also, of course, for some applications where the auxiliary winding is placed in the core slots prior to the main winding (e.g., an inverted winding arrangement), at least one coil side of the auxiliary winding rather than those of the main winding would be provided with the at least 80% slot space factors.

Thus, while there have been described above the principles of this invention in connection with a specific embodiment, it is to be clearly understood that this description is made only by way of example and not as a limitation to the scope of the invention.

What I claim as new and desire to secure by Letters Patent of the United States is:

1. In a stator assembly for a single phase induction motor, a magnetic stator core member having a plurality of winding slots each having a closed end formed therein, a first field winding disposed in predetermined ones of said slots and forming a predetermined number of first poles, a second field winding disposed in predetermined ones of said slots and forming the same predetermined number of second poles respectively angularly displaced from said first poles by a predetermined amount, each of said poles comprising a plurality of concentric coils of progressively greater pitch each formed of a preselected number of turns of wire, each coil of each said first pole occupying a difierent pair of said slots, each coil of each said second pole occupying a different pair of said slots, at least one side of certain coils of each said first pole sharing a selected slot with the side of a coil of a second pole, and means for connecting said first and second windings, respectively, for energization with phase-displaced currents, the number of turns of wire in each of said coils being preselected so that the algebraic product of the third harmonic effective first and second winding turns is in the range from a relatively small positive number to a relatively large negative number and the algebraic product of the fifth harmonic effective first and second winding turns is in the range from a relatively small negative number to a relatively large positive number, said selected shared slots being substantially filled with the wire forming said coil sides, at least one coil side of the first winding in at least one of said selected shared slots being disposed at the closed end thereof with a respective coil side of the second winding placed thereover, said coil side at the closed end of the slot having a space factor of at least 80%.

2. The stator assembly of claim 1 wherein the coil of smallest pitch of each of said first poles has fewer turns than the coil of greatest pitch.

3. The stator assembly of claim 2 wherein the coils of each of said second poles have a progressively greater number of turns from the coil of smallest pitch to the coil of greatest pitch.

4. The stator assembly of claim 2 wherein the coils of each of said poles of at least one winding have a progressively greater number of turns from the coil of smallest pitch to at least the coil of next-to-greatest pitch.

5. The stator assembly of claim 4 wherein the coils of each of said second poles have a progressively greater number of turn-s from the coil of smallest pitch to the coil of greatest pitch, one side of at least the coils of next-to-smallest and smallest pitch, respectively, of at least one of the first poles sharing slots with one side of the coils of smallest and next-to-smallest pitch, respectively, of one of the second poles, one side of the coils of progressively greatest to smallest pitch, respectively, of another one of the second poles sharing slots with the other sides of the coil of progressively smallest to larger pitch, respectively of said one first pole.

6. In a stator assembly for a single phase induction motor, a magnetic stator core member having a plurality of winding slots formed therein, a main field winding disposed in predetermined ones of said slots and forming a predetermined number of main poles, a starting field winding disposed in predetermined ones of said slots and forming the same predetermined number of auxiliary poles respectively angularly displaced from said main poles by a predetermined amount, each of said poles comprising a plurality of concentric coils of progressively greater pitch each formed of a preselected number of turns of wire, each coil of each said main pole occupying a different pair of said slots, each coil of each said auxiliary pole occupying a different pair of said slots, at least one side of certain coils of each said main pole sharing the same slot with the side of a coil of an auxiliary pole, and means for connecting said main and starting windings, respectively, for energization with phasedisplaced currents, the number of turns of wire in each of said coils being preselected so that the algebraic prodnot of the third harmonic effective main and starting winding turns is in the range from a relatively small positive number to a relatively large negative number and the algebraic product of the fifth harmonic effective main and starting winding turns is in the range from a relatively small negative number to a relatively large positive number, said shared slots being substantially filled with the wire forming said coil sides, at least one coil side of one of said windings in said shared slots having a space factor of at least said main pole coil sides being disposed at the bottom of the respective shared slots with the respective auxiliary pole coil sides placed thereover, and said main pole coil sides being compacted in said shared slots to provide said space factor thereby to accommodate said auxiliary pole coil sides.

7. The stator assembly of claim 6 wherein the wire forming at least some of said main pole coils is of aluminum material.

8. The stator assembly of claim 1 wherein said first pole coil sides are disposed at the bottom of the respective shared slots with the respective second pole coil sides placed thereover, said first pole coil sides being compacted in said shared slots to provide said space factor thereby to accommodate said second pole coil sides.

9. The stator assembly of claim 8 wherein the wire forming at least some of said first pole coils is of aluminum material.

10. In a stator assembly for a single phase induction motor, a magnetic stator core member having a plurality of winding slots formed therein, a main field winding disposed in predetermined ones of said slots and forming a predetermined number of main poles, a starting field winding disposed in predetermined ones of said slots and forming the same predetermined number of auxiliary poles respectively angularly displaced from said main poles by a predetermined amount, each of said poles comprising a plurality of concentric coils of progressively greater pitch each formed of a preselected number of turns of wire, each coil of each said main pole occupying a different pair of said slots, each coil of each said auxiliary pole occupying a different pair of said slots, at least one side of certain coils of each said main pole sharing the same slot with the side of a coil of an auxiliary pole, and means for connecting said main and starting windings, respectively, for energization with phasedisplaced currents, the number of turns of wire in each of said coils being preselected so that in the formula:

where ALRT=change in locked rotor torque rv=order of harmonic K =positive constants, functions of n, for a given design N =effective main winding turns for the n harmonic =M sin Har i-M sin (1 M sin na M =number of turns in the respective main coil a /2 the coil pitch angle of the respective main coil in fundamental electrical degrees N =effective starting winding turns for the n harmonic =8 sin n6 +S sin 116 +S sin nfi S =number of turns of the respective starting coil 6 /2 the coil pitch angle of the respective starting coil in fundamental electrical degrees.

The factor K N N is a minimum and the factor K N N is a maximum, said shared slots being substantially filled with wire forming said coil sides, at least one side of said main pole coils in said shared slots having a space factor of at least 80%.

11. In a stator assembly for a single phase induction motor, a magnetic stator core member having a plurality of winding slots formed therein, a first field winding disposed in predetermined ones of said slots and forming a predetermined number of first poles, a second field wind ing disposed in predetermined ones of said slots and forming the same predetermined number of second poles respectively angularly displaced from said first poles by a predetermined amount, each of said poles comprising a plurality of concentric coils of progressively greater pitch each formed of a preselected number of turns of wire, each coil of each of said first poles occupying a different pair of said slots, each coil of each of said second poles occupying a diiferent pair of said slots, at least one side of certain coils of each of said first poles sharing a selected slot with the side of a coil of a second pole, and means for connecting said first and second windings, respectively, for energization with phase-displaced currents, the number of turns of wire in each of said coils being preselected so that in the formula:

where ALRT=change in locked rotor torque rn=order of harmonic K =positive constants, functions of n, for a given design N =eifective first winding turns for the n harmonic =M sin ma l-M sin na M sin not M =number of turns in the respective first coil a /z the coil pitch angle of the respective first coil in fundamental electrical degrees N =effective second winding turns for the n harmonic ==S sin n6 +S sin n6 sin ne S =number of turns of the respective second coil 6 /2 the coil pitch angle of the respective second coil in fundamental electrical degrees,

the factor K N N is a minimum or the factor 5 5e 5es References Cited UNITED STATES PATENTS 3,042,821 7/1962 Stoll 310-166 3,062,978 11/1962 Smith 310--166 3,200,317 8/ 1965 Brammerlo 318-220 3,413,717 12/1968 Peters 310-184 MILTON O. HIRSHFIELD, Primary Examiner R. SKUDY, Assistant Examiner US. Cl. X.R. 

